ABSTRACT
This chapter formalizes the notion of a system. In its most general form, a system takes an input signal and transforms it into an output signal. In mathematical texts a system is sometimes called a functional. A system or functional is much more complicated than a function. It is useful to categorize systems in terms of mathematical properties which they follow, since the models which can be used to describe a system depend upon which properties they exhibit. The convolution model assumes that systems be linear and time invariant. The differential equations model and the linear algebra model assume that systems are linear. There are many systems which are not linear, but which can be made linear using some mathematical transformation. Another important property which a system can have is time invariance. Time invariance means that the system does not change over time. The system function of a linear, time invariant system is one dimensional.
